The speed of a train equipped with an ATC device is controlled by instructions given to the train from a signal section continuously laid out on the ground in the direction of movement of the train. When the train receives a signal instructing it to run within a particular speed range in one signal section, in this signal section the train is controlled so as to run at a speed in the range according to said signal. If the speed as set by the instructions is exceeded, the ATC device detects the excess speed and the train is automatically braked so that the train speed will diminish to the proper value at least before the train reaches the end of said signal section.
If a train moves into the next section at a speed above the upper limit of the speed allowed in one section and instructions for a lower speed are given for said next section, then an instruction will be issued to apply a braking force large enough to brake the train to a speed lower than the speed according to the instruction. Said braking force is usually of a specific magnitude. In the case of an ATC device for the high speed Tokyo-Osaka-Hiroshima line and some other lines in Japan, the braking force is designed to be variable in preset speed ranges. Even with such an arrangement, however, the braking force caused to be exerted by the ATC device is specific within a specific speed range. The magnitude of this specific braking force is selected on the assumption that the train runs to the section boundary at the upper limit of the range of speeds in the preceding section. Therefore, even when the train speed exceeds the speed set by the instructions by only a small amount, a large braking force may act and in most such cases the speed of the train is decelerated to an extent more than necessary. Moreover, the speed of the train approaching the boundary may not be near the upper limit, so that the braking force appropriate for such an upper limit speed is not appropriate for lower speeds. This frequently results in excessive reduction of the ride comfort and the running speed and possible damage to the wheels which may skid during such braking.